{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:6NLB4DT63KUOMOSCSUJDC7CKQX","short_pith_number":"pith:6NLB4DT6","canonical_record":{"source":{"id":"nlin/0211045","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"nlin.CD","submitted_at":"2002-11-27T08:57:45Z","cross_cats_sorted":[],"title_canon_sha256":"2d1a8d553b194a17fa45555737723bd958acd24a3fc457cbe6b16a23de0a25d7","abstract_canon_sha256":"19bdb41b4b4144201fe266771156a0ef4163e7cc76aba57fb7fec7282ced7b1f"},"schema_version":"1.0"},"canonical_sha256":"f3561e0e7edaa8e63a429512317c4a85de821d44e57556a9639392f7458234ae","source":{"kind":"arxiv","id":"nlin/0211045","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0211045","created_at":"2026-07-04T15:02:07Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0211045v1","created_at":"2026-07-04T15:02:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0211045","created_at":"2026-07-04T15:02:07Z"},{"alias_kind":"pith_short_12","alias_value":"6NLB4DT63KUO","created_at":"2026-07-04T15:02:07Z"},{"alias_kind":"pith_short_16","alias_value":"6NLB4DT63KUOMOSC","created_at":"2026-07-04T15:02:07Z"},{"alias_kind":"pith_short_8","alias_value":"6NLB4DT6","created_at":"2026-07-04T15:02:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:6NLB4DT63KUOMOSCSUJDC7CKQX","target":"record","payload":{"canonical_record":{"source":{"id":"nlin/0211045","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"nlin.CD","submitted_at":"2002-11-27T08:57:45Z","cross_cats_sorted":[],"title_canon_sha256":"2d1a8d553b194a17fa45555737723bd958acd24a3fc457cbe6b16a23de0a25d7","abstract_canon_sha256":"19bdb41b4b4144201fe266771156a0ef4163e7cc76aba57fb7fec7282ced7b1f"},"schema_version":"1.0"},"canonical_sha256":"f3561e0e7edaa8e63a429512317c4a85de821d44e57556a9639392f7458234ae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:02:08.000014Z","signature_b64":"jyjQeOOlJ0HBVqEMmAerbpqsXMseEERFYFijNDwpnw8B17i/Ie25fuh9UYjK6W8ypjtQhVnA9GfcDpRJFe1vDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3561e0e7edaa8e63a429512317c4a85de821d44e57556a9639392f7458234ae","last_reissued_at":"2026-07-04T15:02:07.999612Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:02:07.999612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"nlin/0211045","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:02:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZtoZD0MmSivkrsZ3WpVRd6OkWfk6rXdGTlOi+mkkKbypWvBV9Kbx2BhVGfhodJBeMbQO1koSwdpmvyLL972GAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T12:52:40.069404Z"},"content_sha256":"e4e344f8d765080900e30fce8e6f7d1e58310837e1ea1b06bfb1fd76d783197a","schema_version":"1.0","event_id":"sha256:e4e344f8d765080900e30fce8e6f7d1e58310837e1ea1b06bfb1fd76d783197a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:6NLB4DT63KUOMOSCSUJDC7CKQX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Gibbs-like measure for single-time, multi-scale energy transfer in stochastic signals and Shell Model of turbulence","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Luca Biferale, Mauro Sbragaglia, Roberto Benzi","submitted_at":"2002-11-27T08:57:45Z","abstract_excerpt":"A Gibbs-like approach for simultaneous multi-scale correlation functions in random, time-dependent, multiplicative processes for the turbulent energy cascade is investigated. We study the optimal log-normal Gibbs-like distribution able to describe the subtle effects induced by non-trivial time dependency on both single-scale (structure functions) and multi-scale correlation functions. We provide analytical expression for the general multi-scale correlation functions in terms of the two-point correlations between multipliers and we show that the log-normal distribution is already accurate enoug"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0211045","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/nlin/0211045/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:02:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"owyDEE9/U5C9eFLmhUwaAmPZXC2wwt18pXen3B3Jho2UDfQbKWL5Veynqf0fS4y/My6ArutENXjSD2Q5A8LPCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T12:52:40.069915Z"},"content_sha256":"971eab001d08d10c6d3ed5e3e008e64f1d3ce0be55e0209243f68b731d929260","schema_version":"1.0","event_id":"sha256:971eab001d08d10c6d3ed5e3e008e64f1d3ce0be55e0209243f68b731d929260"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6NLB4DT63KUOMOSCSUJDC7CKQX/bundle.json","state_url":"https://pith.science/pith/6NLB4DT63KUOMOSCSUJDC7CKQX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6NLB4DT63KUOMOSCSUJDC7CKQX/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-05T12:52:40Z","links":{"resolver":"https://pith.science/pith/6NLB4DT63KUOMOSCSUJDC7CKQX","bundle":"https://pith.science/pith/6NLB4DT63KUOMOSCSUJDC7CKQX/bundle.json","state":"https://pith.science/pith/6NLB4DT63KUOMOSCSUJDC7CKQX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6NLB4DT63KUOMOSCSUJDC7CKQX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:6NLB4DT63KUOMOSCSUJDC7CKQX","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"19bdb41b4b4144201fe266771156a0ef4163e7cc76aba57fb7fec7282ced7b1f","cross_cats_sorted":[],"license":"","primary_cat":"nlin.CD","submitted_at":"2002-11-27T08:57:45Z","title_canon_sha256":"2d1a8d553b194a17fa45555737723bd958acd24a3fc457cbe6b16a23de0a25d7"},"schema_version":"1.0","source":{"id":"nlin/0211045","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0211045","created_at":"2026-07-04T15:02:07Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0211045v1","created_at":"2026-07-04T15:02:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0211045","created_at":"2026-07-04T15:02:07Z"},{"alias_kind":"pith_short_12","alias_value":"6NLB4DT63KUO","created_at":"2026-07-04T15:02:07Z"},{"alias_kind":"pith_short_16","alias_value":"6NLB4DT63KUOMOSC","created_at":"2026-07-04T15:02:07Z"},{"alias_kind":"pith_short_8","alias_value":"6NLB4DT6","created_at":"2026-07-04T15:02:07Z"}],"graph_snapshots":[{"event_id":"sha256:971eab001d08d10c6d3ed5e3e008e64f1d3ce0be55e0209243f68b731d929260","target":"graph","created_at":"2026-07-04T15:02:07Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/nlin/0211045/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A Gibbs-like approach for simultaneous multi-scale correlation functions in random, time-dependent, multiplicative processes for the turbulent energy cascade is investigated. We study the optimal log-normal Gibbs-like distribution able to describe the subtle effects induced by non-trivial time dependency on both single-scale (structure functions) and multi-scale correlation functions. We provide analytical expression for the general multi-scale correlation functions in terms of the two-point correlations between multipliers and we show that the log-normal distribution is already accurate enoug","authors_text":"Luca Biferale, Mauro Sbragaglia, Roberto Benzi","cross_cats":[],"headline":"","license":"","primary_cat":"nlin.CD","submitted_at":"2002-11-27T08:57:45Z","title":"A Gibbs-like measure for single-time, multi-scale energy transfer in stochastic signals and Shell Model of turbulence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0211045","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e4e344f8d765080900e30fce8e6f7d1e58310837e1ea1b06bfb1fd76d783197a","target":"record","created_at":"2026-07-04T15:02:07Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"19bdb41b4b4144201fe266771156a0ef4163e7cc76aba57fb7fec7282ced7b1f","cross_cats_sorted":[],"license":"","primary_cat":"nlin.CD","submitted_at":"2002-11-27T08:57:45Z","title_canon_sha256":"2d1a8d553b194a17fa45555737723bd958acd24a3fc457cbe6b16a23de0a25d7"},"schema_version":"1.0","source":{"id":"nlin/0211045","kind":"arxiv","version":1}},"canonical_sha256":"f3561e0e7edaa8e63a429512317c4a85de821d44e57556a9639392f7458234ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3561e0e7edaa8e63a429512317c4a85de821d44e57556a9639392f7458234ae","first_computed_at":"2026-07-04T15:02:07.999612Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:02:07.999612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jyjQeOOlJ0HBVqEMmAerbpqsXMseEERFYFijNDwpnw8B17i/Ie25fuh9UYjK6W8ypjtQhVnA9GfcDpRJFe1vDA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:02:08.000014Z","signed_message":"canonical_sha256_bytes"},"source_id":"nlin/0211045","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4e344f8d765080900e30fce8e6f7d1e58310837e1ea1b06bfb1fd76d783197a","sha256:971eab001d08d10c6d3ed5e3e008e64f1d3ce0be55e0209243f68b731d929260"],"state_sha256":"51a8427fecfb1dabb402fe92377816640c0acb299a5e07e15edbd66eab999556"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X4fE634SyeSSVfBdlOzvVV/ap+w+Y0evhFlCzl6aNZr5iM6oWfX6AZA9ran4dUetFQhGueXJUDIgzmBLJvKoAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T12:52:40.076989Z","bundle_sha256":"127438e605ae5f852396651444d8ec0d7aa171ecdba57797d3d860088592729e"}}